1. 1 Conditional Extreme Value Theory and Time Varying Copulas: Evidence from Australian and International Financial Markets by CUONG NGUYEN and M. ISHAQ BHATTI School of Economics and Finance La Trobe University, Australia.

2. 2 Research Questions How to create an appropriate multivariate distribution? How to capture dependence structure or Tail Dependence?

3. 3 1.Motivation and the Problem 2.Methods 3.Results 4.Summary Structure of Presentation

4. 4 Normal qq plots of the daily log returns on BMW and Siemens stocks

5. 5 Actual Returns and Simulated Normal Returns

6. 6 Shortcomings of Correlation Embrechts, McNeil, Straumann (1999) and Roberto (2001)… -The variances must be finite or the linear correlation is not defined. -Independence of two random variables implies they are not correlated but zero correlation does not imply independence. -Linear correlation is not invariant under non-linear strictly increasing transformations

7. 7 Questions What appropriate multivariate distributions to model financial data? Which dependence measures to explain the several types of association observed in financial data? How to capture and present dependence structure in a distribution?

8. 8 Dependence Structure ( identical correlation but different dependence structures)

9. 9 Copula Theory - Sklar’s Theorem A copula is a multivariate distribution function F of random variables X1,…,Xn with standard uniform marginal distributions F1,…,Fn; X1 ~ F1, with i=1,…,n. Density of Copula

10. 10 Methods Extreme Value Theory – Generalized Pareto Distribution (GPD) Gaussian Copula and Symmetrised Joe- Clayton Copula The Inference Functions for Margins Method (IFM) for Copula

11. 11 Results Modelling co-movements of stock markets from Australia, US, UK, Japan, Hongkong, Taiwan.

12. 12 UK US Japan Hong Kong

13. 13 Gaussian Copula (GC) AUS-JPGCLinear Correlation 0.35250.3708 AUS-HKGCLinear Correlation 0.42650.4537 JP-HKGCLinear Correlation 0.35500.360 US-HKGCLinear Correlation 0.12220.1139

14. 14 AUS-UK UK-Taiwan

15. 15 JP-HK Taiwan-HK

16. 16 Symmetrised Joe-Clayton Copula (SJC) AUS-UKSJC Upper Tail 0.071 Lower Tail 0.193 AUS-TWSJC Upper Tail 0.0774 Lower Tail 0.0777 UK-HKSJC Upper Tail 0.097 Lower Tail 0.181 AUS-USSJC Upper Tail 0.000 Lower Tail 0.022

17. 17 AUS-US UK-HK

18. 18 AUS-UK AUS-Taiwan

19. 19 Summary Figuring out tail dependence of different stock markets using copula functions Comparing constant and time-varying copulas Using copula functions is an informative and flexible method to model dependence structure.

20. 20 Thank you very much.

21. 21 References Roberto (2001), “Fitting Copula to Data” Cyril and Guegan (2004), “Forecasting VaR and ES using Dynamical System: A Risk Management Strategy” Patton (2004), “Modelling Time-Varying Exchange Rate Dependence Using Conditional Copula” Eric Zivot and Jiahui Wang (2006), “Modelling Financial Timer Series with Splus” Pravin and David (2005), “Copula Modelling: An Introduction for Practitioners” Beatriz and Rafael (2004), “Measuring Financial Risks with Copulas” …